[1] We present a two-dimensional Glacier Drainage System model (GlaDS) that couples distributed and channelized subglacial water flow. Distributed flow occurs through linked cavities that are represented as a continuous water sheet of variable thickness. Channelized flow occurs through Röthlisberger channels that can form on any of the edges of a prescribed, unstructured network of potential channels. Water storage is accounted for in an englacial aquifer and in moulins, which also act as point sources of water to the subglacial system. Solutions are presented for a synthetic topography designed to mimic an ice sheet margin. For low discharge, all the flow is accommodated in the sheet, whereas for sufficiently high discharge, the model exhibits a channelization instability which leads to the formation of a self-organized channel system. The random orientation of the network edges allows the channel system geometry to be relatively unbiased, in contrast to previous structured grid-based models. Under steady conditions, the model supports the classical view of the subglacial drainage system, with low pressure regions forming around the channels. Under diurnally varying input, water flows in and out of the channels, and a rather complex spatiotemporal pattern of water pressures is predicted. We explore the effects of parameter variations on the channel system topology and mean effective pressure. The model is then applied to a mountain glacier and forced with meltwater calculated by a temperature index model. The results are broadly consistent with our current understanding of the glacier drainage system and demonstrate the applicability of the model to real settings.

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Models are proposed for channelized and distributed flow of meltwater at the base of an ice sheet. The volumes of both channel and distributed systems evolve according to a competition between processes that open drainage space (e.g. sliding over bedrock, melting of the ice) and processes that close it (e.g. viscous creep of the ice due to a positive effective pressure). Channels are generally predicted to have lower water pressure and therefore capture water from the surrounding regions of distributed flow. There is a natural length scale associated with the distributed system that determines the width of the bed from which water can be drawn into a channel. It is suggested that this determines the spacing between major channels and that this may be reflected in the spacing of eskers. A more permeable distributed system results in more widely spaced, and therefore larger, channels. Calculations of the flow into the head of a channel reveal that there is a critical discharge necessary for it to form, and provide a criterion for where channels can exist.

Uncertainty remains about how the surface hydrology of the Greenland ice sheet influences its subglacial drainage system, affecting basal water pressures and ice velocities, particularly over intraseasonal and interseasonal timescales. Here we apply a high spatial (200 m) and temporal (1 h) resolution subglacial hydrological model to a marginal (extending~25 km inland), land-terminating,~200 km 2 domain in the Paakitsoq region, West Greenland. The model is based on that by Hewitt (2013) but adapted for use with both real topographic boundary conditions and calibrated modeled water inputs. The inputs consist of moulin hydrographs, calculated by a surface routing and lake-filling/draining model, which is forced with distributed runoff from a surface energy-balance model. Results suggest that the areal density of lake-bottom moulins and their timing of opening during the melt season strongly affects subglacial drainage system development. A higher moulin density causes an earlier onset of subglacial channelization (i.e., water transport through channels rather than the distributed sheet), which becomes relatively widespread across the bed, whereas a lower moulin density results in a later onset of channelization that becomes less widespread across the bed. In turn, moulin density has a strong control on spatial and temporal variations in subglacial water pressures, which will influence basal sliding rates, and thus ice motion. The density of active surface-to-bed connections should be considered alongside surface melt intensity and extent in future predictions of the ice sheet's dynamics.